<p> This thesis consists of a rigorous development of the direct kinematic, small-displacement theory of thin elastic shells. The theory is developed, so as to facilitate a derivation of the equations of compatibility of middle-surface strains. These equations are developed by the kinematic approach and it is shown that this produces a more coherent relation of such equations to the general theory of shells, as no special techniques are required. The equations of compatibility are developed again by the formal Saint-Venant method; this development serves to substantiate the validity of the kinematic approach. At the same time, it provides many useful identities which are then employed as transformation relations, in order to compare the various forms of compatibility equations, as developed by other authors. A general comparison of kinematic shell theory with other nonkinematic methods is undertaken, and appended to the main discussion.</p> / Thesis / Master of Engineering (MEngr)

<p> This thesis proposes to demonstrate, by means of numerieal examples, the applicability of the approximate solution for shallow, spherical, calotte shells enclosing polygonal bases for the purposes of practical design.</p> <p> The theoretical solution is based on a collocation procedure by means of which prescribed boundary conditions are satisfied at discrete boundary points and is derived from the general theory of MUSHTARI and VLASOV in which the transverse shear deformation of the shell is neglected in comparison with its transverse bending and extensional surface deformation.</p> / Thesis / Master of Engineering (MEngr)

The development of low-frequency sonar systems, using for instance a network of autonomous systems in unmanned vehicles, provides a practical means for bistatic measurements (i.e. when the source and receiver are widely separated) allowing for multiple viewpoints of the target of interest. Time-frequency analysis, in particular Wigner-Ville analysis, takes advantage of the evolution time dependent aspect of the echo spectrum to differentiate a man-made target (e.g. elastic spherical shell) from a natural one of the similar shape (e.g. solid). A key energetic feature of fluid loaded and thin spherical shell is the coincidence pattern, or mid-frequency enhancement echoes (MFE), that result from antisymmetric Lamb-waves propagating around the circumference of the shell. This thesis investigates numerically the bistatic variations of the MFE (with respect to the monostatic configuration) using the Wigner-Ville analysis. The observed time-frequency shifts of the MFE are modeled using a previously derived quantitative ray theory for spherical shell's scattering. Additionally, the advantage of an optimal array beamformer, based on joint time delays and frequency shifts (over a conventional time-delay beamformer) is illustrated for enhancing the detection of the MFE recorded across a bistatic receiver array.